A roller in a printing press turns through an angle `theta=3t^(2)-t^(3) rad`.
(a) Calculate the angular velocity and angular acceleration as a function of time `t`.
(b) What is the maximum positive angular velocity and at what time `t` does it occur?

Explanation

(a) `theta=3t^(2)-t^(3)`
`omega=(d theta)/(dt)=6t-3t^(2)`
`alpha=(domega)/(dt)=6-6t`
(b) `omega` is maximum when `alpha=(domega)/(dt)=0`
`6-6t = 0 implies t = 1 s`
`omega_(max)=6(1)-3(1)^(2)= 3 rad//s`